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SUMMARY:K.R. Helfrich*\, L.A. Ostrovsky **\, Yu.A. Stepanyants*** (* Depar
 tment of Physical Oceanography\, Woods Hole Oceanographic Institution\, Wo
 ods Hole\, MA USA. ** Department of Applied Mathematics\, University of Co
 lorado\, Boulder\, CO\, USA. *** School of Mathematics\, Physics and Compu
 ting\, University of Southern Queensland\, Toowoomba\, QLD\, 4350\, Austra
 lia)
DTSTART:20220512T120000Z
DTEND:20220512T130000Z
DTSTAMP:20260423T021329Z
UID:mmandim/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/41/"
 >Joint Effects of Rotation and Topography on Internal Solitary Waves</a>\n
 by K.R. Helfrich*\, L.A. Ostrovsky **\, Yu.A. Stepanyants*** (* Department
  of Physical Oceanography\, Woods Hole Oceanographic Institution\, Woods H
 ole\, MA USA. ** Department of Applied Mathematics\, University of Colorad
 o\, Boulder\, CO\, USA. *** School of Mathematics\, Physics and Computing\
 , University of Southern Queensland\, Toowoomba\, QLD\, 4350\, Australia) 
 as part of Mathematical models and integration methods\n\n\nAbstract\nWe p
 resent the results of the recent study of dynamics of nonlinear oceanic so
 litary waves under the influence of the combined effects of nonlinearity\,
  Earth’s rotation\, and depth inhomogeneity. Our consideration is based 
 on the extended model of the Korteweg–de Vries (KdV) equation that in ge
 neral accounts for the quadratic and cubic nonlinearity (the Gardner equat
 ion) with the additional terms incorporating the effects of rotation and s
 lowly varying depth. After a brief historical outline\, using the asymptot
 ic (adiabatic) theory\, we describe a complex interplay between these fact
 ors. As an application\, the case of a two-layer fluid with the variable-d
 epth lower layer is considered using the approximate theory\, as well as t
 hrough numerical solutions of the governing equation that includes all the
  above factors under realistic oceanic conditions. In particular\, differe
 nt scenarios of the soliton propagating toward the “internal beach” (e
 .g.\, zero lower-layer depth) are studied in which the terminal damping ca
 n be caused by radiation or disappearing quadratic nonlinearity (when the 
 layers’ depths become equal). We also consider interaction of a soliton 
 with a long wave providing the energy “pump” compensating the radiatio
 n losses due to rotation so that the soliton can exist infinitely. The lim
 itations of the adiabatic approach due to the radiation and other factors 
 are also demonstrated.\n
LOCATION:https://researchseminars.org/talk/mmandim/41/
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